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Subcriticality and gaugeability of the Schrödinger operator. (English) Zbl 0765.60063

The Schrödinger operator \(H=-\Delta/2+V\) in \(R^ d\), \(d\geq 3\), with a potential \(V\) in the Kato class \(K_ d\) is considered and conditions on subcriticality, strong positivity and gaugeability of such operators are studied. It is shown that for large classes of potentials these conditions are equivalent. Various sufficient conditions of such equivalence are elaborated.

MSC:

60H25 Random operators and equations (aspects of stochastic analysis)
60J65 Brownian motion
81S40 Path integrals in quantum mechanics
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